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Submitted by plusadmin on September 1, 2005

September 2005

A knight's nightmare

Imagine a chess board with squares, on each side. Now imagine a knight moving around the board - only using the moves that are allowed to a knight of course - so that each square of the board is visited exactly once, and so that the knight ends up on the same square as it started. Such a tour is called a closed knight's tour (it's closed because
the knight ends where it started). If you start experimenting on an ordinary chess board, you'll soon see that it's no easy feat to find a closed knight's tour. People have been entertaining themselves with this pursuit for centuries. The earliest recorded example of a knight's tour on the ordinary board came from al-Adli ar-Rumi, who lived in Baghdad around 840AD.
There are also example of knight's tours of But no-one has ever found a closed knight's tour on an board when is odd. Can you prove why this is, in fact, impossible? Hint

If you're poetically minded, try this one: find a knight's tour on this board, so that the syllables on the squares, when read in the sequence of the tour, form a verse (note that this time you're not asked for a closed knight's tour - it does not have to end at the same place it started). Hint

With

white

-gle

from

-lant

black

a

star-

square

the

knight

and

sin-

-ted

gal-

of

did

nerve

And

-where

And

twice

He

-sing

prove

Nor

king's

on

it

-ny

land

A

of

once

he

back

-ting

-main

mis-

might

came

to

res-

do-

a-

to

fire

the

a-

steel

his

-gain

To

heart

-full

-out

all

a-

-spire

and

power-

With-

roam

of

This puzzle was published in 1884 in the book Chess Fruits by T. B. Rowlands and his wife Frideswide F. Rowlands. Crossword puzzles had not been invented at that time, and this kind of puzzle was very popular.